In an aerial hybrid massive multiple-input multiple-output (MIMO) and orthogonal frequency division multiplexing (OFDM) system, how to design a spectral-efficient broadband multi-user hybrid beamforming with a limited pilot and feedback overhead is challenging. To this end, by modeling the key transmission modules as an end-to-end (E2E) neural network, this paper proposes a data-driven deep learning (DL)-based unified hybrid beamforming framework for both the time division duplex (TDD) and frequency division duplex (FDD) systems with implicit channel state information (CSI). For TDD systems, the proposed DL-based approach jointly models the uplink pilot combining and downlink hybrid beamforming modules as an E2E neural network. While for FDD systems, we jointly model the downlink pilot transmission, uplink CSI feedback, and downlink hybrid beamforming modules as an E2E neural network. Different from conventional approaches separately processing different modules, the proposed solution simultaneously optimizes all modules with the sum rate as the optimization object. Therefore, by perceiving the inherent property of air-to-ground massive MIMO-OFDM channel samples, the DL-based E2E neural network can establish the mapping function from the channel to the beamformer, so that the explicit channel reconstruction can be avoided with reduced pilot and feedback overhead. Besides, practical low-resolution phase shifters (PSs) introduce the quantization constraint, leading to the intractable gradient backpropagation when training the neural network. To mitigate the performance loss caused by the phase quantization error, we adopt the transfer learning strategy to further fine-tune the E2E neural network based on a pre-trained network that assumes the ideal infinite-resolution PSs. Numerical results show that our DL-based schemes have considerable advantages over state-of-the-art schemes.

中文翻译：

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用于具有隐式 CSI 的空中大规模 MIMO-OFDM 系统的基于数据驱动的深度学习的混合波束成形

在空中混合大规模多输入多输出 (MIMO) 和正交频分复用 (OFDM) 系统中，如何设计具有有限导频和反馈开销的频谱高效的宽带多用户混合波束成形具有挑战性。为此，通过将关键传输模块建模为端到端（E2E）神经网络，本文提出了一种基于数据驱动的深度学习（DL）的统一混合波束成形框架，适用于时分双工（TDD）和具有隐式信道状态信息 (CSI) 的频分双工 (FDD) 系统。对于 TDD 系统，所提出的基于 DL 的方法将上行链路导频组合和下行链路混合波束成形模块联合建模为 E2E 神经网络。而对于 FDD 系统，我们联合建模下行导频传输、上行 CSI 反馈、和下行链路混合波束成形模块作为 E2E 神经网络。与传统方法分别处理不同的模块不同，所提出的解决方案以总和率作为优化对象同时优化所有模块。因此，通过感知空对地大规模 MIMO-OFDM 信道样本的固有属性，基于 DL 的 E2E 神经网络可以建立从信道到波束形成器的映射函数，从而避免显式信道重建，减少试点和反馈开销。此外，实用的低分辨率移相器（PSs）引入了量化约束，导致在训练神经网络时难以处理梯度反向传播。为了减轻相位量化误差引起的性能损失，我们采用迁移学习策略来进一步微调基于预训练网络的 E2E 神经网络，该网络假设理想的无限分辨率 PS。数值结果表明，我们基于 DL 的方案比最先进的方案具有相当大的优势。